Abstract

Multiple passages of light through an absorption inhomogeneity of finite size deep within a turbid medium are analyzed for optical imaging by use of the self-energy diagram. The nonlinear correction becomes more important for an inhomogeneity of a larger size and with greater contrast in absorption with respect to the host background. The nonlinear correction factor agrees well with that from Monte Carlo simulations for cw light. The correction is approximately 50%–75% in the near infrared for an absorption inhomogeneity with the typical optical properties found in tissues and five times the size of the transport mean free path.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Yodh and B. Chance, Phys. Today 48(3), 38 (1995).
  2. S. R. Arridge, Inverse Probl. 15, R41 (1999).
    [CrossRef]
  3. A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, and R. Nossal, Appl. Opt. 37, 1973 (1998).
    [CrossRef]
  4. W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, and R. R. Alfano, Appl. Opt. 38, 4237 (1999).
    [CrossRef]
  5. S. Carraresi, T. S. M. Shatir, F. Martelli, and G. Zaccanti, Appl. Opt. 40, 4622 (2001).
    [CrossRef]
  6. J. W. Negele and H. Orland, Quantum Many-Particle Systems (Westview, Boulder, Colo., 1998).
  7. M. Xu, W. Cai, M. Lax, and R. R. Alfano, Opt. Lett. 26, 1066 (2001).
    [CrossRef]
  8. W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 61, 3871 (2000).
    [CrossRef]
  9. A. Guinier, G. Fournet, C. B. Walker, and K. L. Yudowitch, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).
  10. M. Testorf, U. Osterberg, B. Pogue, and K. Paulsen, Appl. Opt. 38, 236 (1999).
    [CrossRef]
  11. M. Xu, W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 65, 066609 (2002).
    [CrossRef]
  12. H. Rief, J. Comput. Phys. 111, 33 (1994).
    [CrossRef]
  13. V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
    [CrossRef] [PubMed]
  14. W. F. Cheong, S. Prahl, and A. J. Welch, IEEE J. Quantum Electron. 26, 2166 (1990).
    [CrossRef]

2002

M. Xu, W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 65, 066609 (2002).
[CrossRef]

2001

2000

W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 61, 3871 (2000).
[CrossRef]

1999

1998

1995

A. Yodh and B. Chance, Phys. Today 48(3), 38 (1995).

1994

H. Rief, J. Comput. Phys. 111, 33 (1994).
[CrossRef]

1990

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

W. F. Cheong, S. Prahl, and A. J. Welch, IEEE J. Quantum Electron. 26, 2166 (1990).
[CrossRef]

Alfano, R. R.

Alrubaiee, M.

Arridge, S. R.

S. R. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

Cai, W.

Carraresi, S.

Chance, B.

A. Yodh and B. Chance, Phys. Today 48(3), 38 (1995).

Cheong, W. F.

W. F. Cheong, S. Prahl, and A. J. Welch, IEEE J. Quantum Electron. 26, 2166 (1990).
[CrossRef]

Chernomordik, V.

Fournet, G.

A. Guinier, G. Fournet, C. B. Walker, and K. L. Yudowitch, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

Gayen, S. K.

Guinier, A.

A. Guinier, G. Fournet, C. B. Walker, and K. L. Yudowitch, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).

Hebden, J. C.

Lax, M.

Martelli, F.

Negele, J. W.

J. W. Negele and H. Orland, Quantum Many-Particle Systems (Westview, Boulder, Colo., 1998).

Nossal, R.

Orland, H.

J. W. Negele and H. Orland, Quantum Many-Particle Systems (Westview, Boulder, Colo., 1998).

Osterberg, U.

Patterson, M. S.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Paulsen, K.

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Pogue, B.

Prahl, S.

W. F. Cheong, S. Prahl, and A. J. Welch, IEEE J. Quantum Electron. 26, 2166 (1990).
[CrossRef]

Rief, H.

H. Rief, J. Comput. Phys. 111, 33 (1994).
[CrossRef]

Shatir, T. S. M.

Testorf, M.

Walker, C. B.

A. Guinier, G. Fournet, C. B. Walker, and K. L. Yudowitch, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).

Welch, A. J.

W. F. Cheong, S. Prahl, and A. J. Welch, IEEE J. Quantum Electron. 26, 2166 (1990).
[CrossRef]

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Xu, M.

Yodh, A.

A. Yodh and B. Chance, Phys. Today 48(3), 38 (1995).

Yudowitch, K. L.

A. Guinier, G. Fournet, C. B. Walker, and K. L. Yudowitch, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).

Zaccanti, G.

Zevallos, M.

Appl. Opt.

IEEE J. Quantum Electron.

W. F. Cheong, S. Prahl, and A. J. Welch, IEEE J. Quantum Electron. 26, 2166 (1990).
[CrossRef]

Inverse Probl.

S. R. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

J. Comput. Phys.

H. Rief, J. Comput. Phys. 111, 33 (1994).
[CrossRef]

Opt. Lett.

Phys. Med. Biol.

V. G. Peters, D. R. Wyman, M. S. Patterson, and G. L. Frank, Phys. Med. Biol. 35, 1317 (1990).
[CrossRef] [PubMed]

Phys. Rev. E

M. Xu, W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 65, 066609 (2002).
[CrossRef]

W. Cai, M. Lax, and R. R. Alfano, Phys. Rev. E 61, 3871 (2000).
[CrossRef]

Phys. Today

A. Yodh and B. Chance, Phys. Today 48(3), 38 (1995).

Other

A. Guinier, G. Fournet, C. B. Walker, and K. L. Yudowitch, Small-Angle Scattering of X-Rays (Wiley, New York, 1955).

J. W. Negele and H. Orland, Quantum Many-Particle Systems (Westview, Boulder, Colo., 1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Self-propagator N¯selfω;RVlt-1c and its approximation form when κ=0. (b) Self-propagator for spheres of various radii in the time domain inside a nonabsorbing medium.

Fig. 2
Fig. 2

NCF (magnitude and phase angle) versus the size of absorbers whose excess absorption δμalt/c equals 0.01 and 0.05. Note that κ2lt2=3μa-iωlt/c for the background medium.

Fig. 3
Fig. 3

(a) Theoretical nonlinear correction factors from numerical quadrature (Exact), the approximate form of relation (7) (Approx), and Monte Carlo simulations (MC). Results from four independent Monte Carlo simulations are shown for each radius. The standard linear perturbation approach corresponds to horizontal line NCF=1 (not shown in the figure). (b) Percentage change of the cw transmittance from the experimental data given in Fig. 9 of Ref. 5 compared with the theoretical predictions made by the standard linear perturbation approach (StdPert) and those including NCF (Exact and Approx).

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ΔI=-Grd,ωr¯Vδμar¯n=0-N¯selfω;RVδμar¯n×Gr¯,ωrs=-Grd,ωr¯Vδμar¯1+N¯selfω;RVδμar¯×Gr¯,ωrs,
N¯selfω;R=1V2VVGr2,ωr1d3r2d3r1
NCF=1+N¯selfω;RVδμar¯-1.
Neffr,ω14πr2cexp-13κ2ltr+exp-κlt4πDrκltsinhκr,r<ltexp-κr4πDrκltsinhκlt,rlt,
N¯selfω;R=1V2VVNeffr2-r1,ωd3r2d3r1=1V02RNeffr,ωγ0r4πr2dr,
N¯selfω;R=ltVc×34ξ+ξ3-ξ3κlt+Oκ2,ξ1/265ξ2+12-316ξ-1+3320ξ-3-ξ3κlt+Oκ2,ξ>1/2,
NCF1+916πqξ-2+43-1,ξ1/2[1+910πq(ξ-1+512ξ-3 -532ξ-4+1128ξ-6)]-1,ξ>1/2,

Metrics